Linganisha mbinu

	Uchanganuzi wa Bayesian wa Takriban	Uchanganuzi wa Mfumo wa Markov wa Monte Carlo (MCMC)
Nyanja	Uigaji	Uigaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	2002	1953 (Metropolis-Hastings); 1984 (Gibbs)
Mwanzilishi	—	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)
Aina	Simulation-based Bayesian inference	Simulation-based Bayesian inference / numerical integration
Chanzo asilia	Beaumont, M.A., Zhang, W. & Balding, D.J. (2002). Approximate Bayesian Computation in Population Genetics. Genetics, 162(4), 2025-2035.	Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. & Rubin, D.B. (2013). Bayesian Data Analysis (3rd ed.). Chapman & Hall/CRC.
Majina mbadala	ABC, likelihood-free inference, simulation-based inference, Yaklaşık Bayesçi Hesaplama (ABC)	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)
Zinazohusiana	5	5
Muhtasari	Approximate Bayesian Computation (ABC) is a family of simulation-based inference methods that estimate posterior distributions without requiring an analytically tractable likelihood function. Introduced by Beaumont, Zhang and Balding (2002) in the context of population genetics, ABC replaced the intractable likelihood with repeated model simulation and a comparison of summary statistics between simulated and observed data.	Markov Chain Monte Carlo (MCMC) is a family of simulation algorithms that constructs a Markov chain whose stationary distribution is the target posterior, enabling Bayesian inference and high-dimensional integral computation that would otherwise be analytically intractable. Pioneered by Metropolis and colleagues in 1953 and extended by Hastings in 1970, MCMC underpins modern Bayesian statistics. The two most widely used variants are Metropolis-Hastings, which proposes moves from a general proposal distribution, and Gibbs sampling, which draws each parameter in turn from its full conditional distribution.